Examples 6-13 contain a selection of grids and diatonic scales from other Cn scales.
Examples 12 and 13 are C19 and C31 seven-tone diatonic scales. These are included to show that the grid technique for the creation of new diatonic scales can also generate the same diatonic scale as best fir to just-intonation-ratio methods.
What was said above about the new C20 diatonic scale also applies to these new diatonic scales: notation and harmonic structure should only be proposed after investigation of the acoustic materials.
The C19 and C31 diatonic scales led me to the following conclusion: For all valid diatonic scales, the two intervals in the grid approximate to a given pair of just intonation ratios.
I believe that the diatonic scales derived from the different Cn scales conform to background formations existing independently of the number of tones in the base Cn scale.
By joining the seven notes of the diatonic scale, a chordal structure is produced in the figure.
The result is a seven-note diatonic scale which is supposed to improve consonance in string ensembles (Elster 1991).
By now, every reader should be convinced that the eleven-note scale is the correct analogue of the seven-note diatonic scale in the twelve-tone system, but one more piece of evidence is still available.
I now use the Balzano diagram, as described at the end of Section I, to identify the major and natural minor modes of our diatonic scale. I shall call the five chords appropriate to each mode the sub-sub-dominant, the sub-dominant, the tonic, the dominant and the super-dominant.
What I am saying is that while the descriptions of beat and twelve-equal-temperament hearings, and the descriptions of the melodic and rhythmic grouping hearings, on the one hand, are objective, the descriptions of metre and diatonic scale steps hearings, on the other hand, are always subjective.
Again the diatonic scale hearing is parallel to the metre hearing.
Firstly, as a beautiful object is traditionally defined as an object which is pleasurable to look at, we may say that hearing sounds as subsumed by the diatonic scale and as melodically grouped together results in pleasure.